Deriving the Equation for Two-Body Mass Interaction for Scientists

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The discussion centers on deriving the equation T=m[1]m[2]g/(m1+m2), which is related to tension in a string connecting two masses. Participants emphasize the need for clarity regarding the equation's context and the meanings of its variables. It is suggested that the problem likely involves a coupled-mass system with one mass hanging off a frictionless surface. To derive the equation, free-body diagrams should be drawn, and Newton's laws of motion applied. Clear communication of the problem is essential for effective assistance.
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T=m[1]m[2]g/(m1+m2)
 
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Welcome to PF;
It is impossible to derive the equation from the information (none) given.
We need to know what the equation is supposed to represent and what all the letters mean.

It looks kinda like a coupled-mass relationship, where one mass is hanging off a frictionless surface, and you are solving for the tension in the string connecting them.
That's just a guess - don't make people guess what you are asking. If the guess is good, then you start by drawing free-body diagrams for the masses like you were taught in school and apply Newton's laws.
 
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Sorry
First being new member it happens so.

It is the equation of tension in a string .
I mean how to derive the equation of tension in a string ?
 
Just like I said - draw free body diagrams and apply Newton's laws of motion.
 

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